Based on design algorithms of hard X-ray spectrometers in advanced light sources around the world, high energy resolution is realized by adopting cylindrically bent Bragg crystals. A new structure of a double diffraction spectrometer is proposed, which can achieve 2×10 ⁵ energy resolution of single pulse in the photon energy range of 3--25 keV. The energy resolution performance of the spectrometer is verified by theoretical analysis and numerical calculation. And a broad spectrum with bandwidth beyond 1% can be reconstructed via mechanical scan. This technique can potentially be used to measure the fine structure in self-amplified spontaneous emission (SASE) spectra within hard X-ray spectral range for Shanghai High Repetition Rate hard X-ray free electron laser (XFEL) and Extreme Light Facility (SHINE), and it can be applied to detection and application of the cutting edge user scientific researches demanding high resolving power, preserving important merit of value in science and technology.